Automatic Matching of Full and Degraded Bullet Lands

Outline

Same Source Problem: were two bullets fired through the same gun barrel?
Besides visual inspection: score from Automatic Matching Algorithm based on 3d topographic images
Score provides objective measure for the match (between 0 and 1, the higher the more likely the match)
Investigate properties of these scores

x3p format: ISO 25178-72:2017

Automated Matching Algorithm: Front-End Web Application

https://isu-csafe.stat.iastate.edu/shiny/bulletr/

Automated Matching Algorithm

initial image processing to extract relevant pattern

Step 1: extract profile

Automated Matching Algorithm

initial image processing to extract relevant pattern

Step 2: identify shoulders

Automated Matching Algorithm

initial image processing to extract relevant pattern

Step 3: long-pass Gaussiam filter

Automated Matching Algorithm

initial image processing to extract relevant pattern

Step 4: get land signature

Automated Matching Algorithm

initial image processing to extract relevant pattern

Step 5: identify peaks

Automated Matching Algorithm

initial image processing to extract relevant pattern

Step 6: align pairs of lands

Automated Matching Algorithm

initial image processing to extract relevant pattern

Step 6 (cont’d): match peaks across lands

Automated Matching Algorithm

initial image processing to extract relevant pattern
algorithm based on features extracted from pairwise comparison of profiles
train algorithm on reference database
get scores for new land-land comparisons

Automated Matching Algorithm: Extract Features

Features are extracted from each land-to-land comparison:

ccf (%) is the maximum value of the Cross-Correlation function evaluated at the optimal alignment. The CCF is defined as \(C(\tau) = \int_{-\infty}^{\infty} f(t)g(t + \tau)dt\) where \(\tau\) represents the the lag of the second signature (T. Vorburger et al. 2011).
D (mm) is the Euclidean vertical distance between each height value of the aligned signatures. This is defined as \(D^2 = 1/n \times \sum_t (f(t) - g(t))^2\). Measure of the total variation (Clarkson and Adams 1933).
matches is the number of matching peaks/valleys (striae) of the overlapping portion of the aligned signatures.

More Features

mismatches is the number of mismatching peaks/valleys (striae) of the overlapping portion of the aligned signatures.
cms is the number of consecutively matching peaks/valleys (striae) of the overlapping portion of the aligned signatures (Biasotti 1959).
non_cms is the number of consecutive mismatching peaks/valleys (striae) of the overlapping portion of the aligned signatures.
S (mm) is the the sum of the average heights of matched striae.

Reference database

James Hamby Study: Ten consecutively rifled Ruger P-85 pistol barrels used to fire 20 “known” test bullets and 15 “unknown” bullets for comparison (Hamby, Brundage, and Thorpe 2009)
Use 3d image of Hamby-252 as reference database to train the algorithm
Extract features for all land-land comparisons (21945 total)
Compare differences in features between 7,075 known matches and 14,040 known non-matches

Distribution of Features

Data-driven rules

data-driven decision rule (classification tree, Breiman et al 1984)
tree creates MATCH/NO-MATCH decision for each pair of lands
in this tree: 1 false positive, 40 false negatives (for pairs of lands)

Algorithm: Forest of 1000 trees

Algorithm is based on 1000 trees, each tree gets a vote

Feature Importance

ccf is good, but better in combination with other features

How much of a land do we need for a match?

Feature Standardization

standardize features by the length of the recovered land
this does not impact full lands, e.g. here: Matches = 27, Matches per mm = 14.72

True Degraded Case

shorter signatures are not penalized (as much) by using standardized features

Here: Matches = 8 (full: 27), Matches per mm = 11.42 (14.72)

Standardized Features

matches (per mm) is the number of matching peaks/valleys (striae) per millimeter of the overlapping portion of the aligned signatures.
mismatches (per mm) is the number of mismatching peaks/valleys (striae) per millimeter of the overlapping portion of the aligned signatures.
cms (per mm) is the number of consecutively matching peaks/valleys (striae) per millimeter of the overlapping portion of the aligned signatures (Biasotti 1959, W. Chu et al. (2013)).
non_cms (per mm) is the number of consecutive mismatching peaks/valleys (striae) per millimeter of the overlapping portion of the aligned signatures.
S (per mm) is the the sum of the average heights of matched striae.

Degraded Bullets

Simulation Study:

Three types of Degradation:
1. Left Fixed - The left portion of the land (leading shoulder) is recoverable.
2. Middle Fixed - The middle portion of the land is recoverable.
3. Right Fixed - The right portion of the land (trailing shoulder) is recoverable.
Six Degradation Levels: 100% (Fully recovered), 87.5% Recovered, 75% Recovered, 62.5% Recovered, 50% Recovered, 37.5% Recovered, 25% Recovered.

Simulation Results

Sensitivity: correctly identify a known match (of a pair of lands)
Specificity: correctly identify a known non-match (of a pair of lands)

Testing this Finding

To come full circle, we will attempt to extract a 50% degraded signature from a Hamby bullet land with bad tank rash in one half. (Barrel 9 Bullet 2 Land 4):

Br924 Results

Extracting the ideal signature and then simulating a left-fixed 50% degradation scenario yields the following:

Reference Database

biggest limitation thus far is limited amount of available 3D scan data for bullets:

in NIST ballistics database (Xiaoyu Alan Zhang, https://tsapps.nist.gov/NRBTD):

Hamby Set 252 (10 Barrels)
Hamby Set 44 (Same 10 Barrels)
Cary Persistence (1 Barrel)

11 unique gun barrels is not yet enough to form a true reference distribution for known matches and non-matches…

…However, the structure of the database means that as soon as new data is available, the features and scores can be easily recomputed.

please contribute your experimental data!

Future work

besides open data we need open algorithms and open results
comparison with other automated matching algorithms, e.g. Scratch
how much variability is introduced due to operator, lab, type of microscope? - great talk by Martin Baiker yesterday!
importance of parameter choices / feature selection

Thank You

Special thanks to Alan Zheng at the National Institute of Standards and Technology for maintaining the NIST Ballistics Toolmark Research Database and providing many useful suggestions.

Announcement

CSAFE is the NIST Center of Excellence in Forensic Sciences.
We are eager to engage the forensic community and get your input.
We are equipped to do 3D imaging of bullets, cartridge cases and other toolmarks and to analyze those images.
IF YOU ARE A FIREARMS examiner and would like to visit Iowa State to learn about 3D surface analysis, please contact us.
We can provide funding for travel and lodging while in Ames. alicia@iastate.edu or hofmann@iastate.edu

References

Biasotti, Alfred A. 1959. “A Statistical Study of the Individual Characteristics of Fired Bullets.” Journal of Forensic Sciences 4 (1): 34–50.

Chu, Wei, Robert M Thompson, John Song, and Theodore V Vorburger. 2013. “Automatic identification of bullet signatures based on consecutive matching striae (CMS) criteria.” Forensic Science International 231 (1–3): 137–41.

Clarkson, James A, and C Raymond Adams. 1933. “On Definitions of Bounded Variation for Functions of Two Variables.” Transactions of the American Mathematical Society 35 (4). JSTOR: 824–54.

Hamby, James E., David J. Brundage, and James W. Thorpe. 2009. “The Identification of Bullets Fired from 10 Consecutively Rifled 9mm Ruger Pistol Barrels: A Research Project Involving 507 Participants from 20 Countries.” AFTE Journal 41 (2): 99–110.

Vorburger, T.V., J.-F. Song, W. Chu, L. Ma, S.H. Bui, A. Zheng, and T.B. Renegar. 2011. “Applications of Cross-Correlation Functions.” Wear 271 (3–4): 529–33. doi:http://dx.doi.org/10.1016/j.wear.2010.03.030.